04e44b37cc
This PR update PySpark to support Python 3 (tested with 3.4). Known issue: unpickle array from Pyrolite is broken in Python 3, those tests are skipped. TODO: ec2/spark-ec2.py is not fully tested with python3. Author: Davies Liu <davies@databricks.com> Author: twneale <twneale@gmail.com> Author: Josh Rosen <joshrosen@databricks.com> Closes #5173 from davies/python3 and squashes the following commits: d7d6323 [Davies Liu] fix tests 6c52a98 [Davies Liu] fix mllib test 99e334f [Davies Liu] update timeout b716610 [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 cafd5ec [Davies Liu] adddress comments from @mengxr bf225d7 [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 179fc8d [Davies Liu] tuning flaky tests 8c8b957 [Davies Liu] fix ResourceWarning in Python 3 5c57c95 [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 4006829 [Davies Liu] fix test 2fc0066 [Davies Liu] add python3 path 71535e9 [Davies Liu] fix xrange and divide 5a55ab4 [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 125f12c [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 ed498c8 [Davies Liu] fix compatibility with python 3 820e649 [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 e8ce8c9 [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 ad7c374 [Davies Liu] fix mllib test and warning ef1fc2f [Davies Liu] fix tests 4eee14a [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 20112ff [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 59bb492 [Davies Liu] fix tests 1da268c [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 ca0fdd3 [Davies Liu] fix code style 9563a15 [Davies Liu] add imap back for python 2 0b1ec04 [Davies Liu] make python examples work with Python 3 d2fd566 [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 a716d34 [Davies Liu] test with python 3.4 f1700e8 [Davies Liu] fix test in python3 671b1db [Davies Liu] fix test in python3 692ff47 [Davies Liu] fix flaky test 7b9699f [Davies Liu] invalidate import cache for Python 3.3+ 9c58497 [Davies Liu] fix kill worker 309bfbf [Davies Liu] keep compatibility 5707476 [Davies Liu] cleanup, fix hash of string in 3.3+ 8662d5b [Davies Liu] Merge branch 'master' of github.com:apache/spark into python3 f53e1f0 [Davies Liu] fix tests 70b6b73 [Davies Liu] compile ec2/spark_ec2.py in python 3 a39167e [Davies Liu] support customize class in __main__ 814c77b [Davies Liu] run unittests with python 3 7f4476e [Davies Liu] mllib tests passed d737924 [Davies Liu] pass ml tests 375ea17 [Davies Liu] SQL tests pass 6cc42a9 [Davies Liu] rename 431a8de [Davies Liu] streaming tests pass 78901a7 [Davies Liu] fix hash of serializer in Python 3 24b2f2e [Davies Liu] pass all RDD tests 35f48fe [Davies Liu] run future again 1eebac2 [Davies Liu] fix conflict in ec2/spark_ec2.py 6e3c21d [Davies Liu] make cloudpickle work with Python3 2fb2db3 [Josh Rosen] Guard more changes behind sys.version; still doesn't run 1aa5e8f [twneale] Turned out `pickle.DictionaryType is dict` == True, so swapped it out 7354371 [twneale] buffer --> memoryview I'm not super sure if this a valid change, but the 2.7 docs recommend using memoryview over buffer where possible, so hoping it'll work. b69ccdf [twneale] Uses the pure python pickle._Pickler instead of c-extension _pickle.Pickler. It appears pyspark 2.7 uses the pure python pickler as well, so this shouldn't degrade pickling performance (?). f40d925 [twneale] xrange --> range e104215 [twneale] Replaces 2.7 types.InstsanceType with 3.4 `object`....could be horribly wrong depending on how types.InstanceType is used elsewhere in the package--see http://bugs.python.org/issue8206 79de9d0 [twneale] Replaces python2.7 `file` with 3.4 _io.TextIOWrapper 2adb42d [Josh Rosen] Fix up some import differences between Python 2 and 3 854be27 [Josh Rosen] Run `futurize` on Python code: 7c5b4ce [Josh Rosen] Remove Python 3 check in shell.py.
889 lines
37 KiB
Python
889 lines
37 KiB
Python
# -*- encoding: utf-8 -*-
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# back ported from CPython 3
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# A. HISTORY OF THE SOFTWARE
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# ==========================
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#
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# Python was created in the early 1990s by Guido van Rossum at Stichting
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# Mathematisch Centrum (CWI, see http://www.cwi.nl) in the Netherlands
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# as a successor of a language called ABC. Guido remains Python's
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# principal author, although it includes many contributions from others.
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#
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# In 1995, Guido continued his work on Python at the Corporation for
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# National Research Initiatives (CNRI, see http://www.cnri.reston.va.us)
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# in Reston, Virginia where he released several versions of the
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# software.
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#
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# In May 2000, Guido and the Python core development team moved to
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# BeOpen.com to form the BeOpen PythonLabs team. In October of the same
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# year, the PythonLabs team moved to Digital Creations (now Zope
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# Corporation, see http://www.zope.com). In 2001, the Python Software
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# Foundation (PSF, see http://www.python.org/psf/) was formed, a
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# non-profit organization created specifically to own Python-related
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# Intellectual Property. Zope Corporation is a sponsoring member of
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# the PSF.
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#
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# All Python releases are Open Source (see http://www.opensource.org for
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# the Open Source Definition). Historically, most, but not all, Python
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# releases have also been GPL-compatible; the table below summarizes
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# the various releases.
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#
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# Release Derived Year Owner GPL-
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# from compatible? (1)
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#
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# 0.9.0 thru 1.2 1991-1995 CWI yes
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# 1.3 thru 1.5.2 1.2 1995-1999 CNRI yes
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# 1.6 1.5.2 2000 CNRI no
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# 2.0 1.6 2000 BeOpen.com no
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# 1.6.1 1.6 2001 CNRI yes (2)
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# 2.1 2.0+1.6.1 2001 PSF no
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# 2.0.1 2.0+1.6.1 2001 PSF yes
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# 2.1.1 2.1+2.0.1 2001 PSF yes
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# 2.2 2.1.1 2001 PSF yes
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# 2.1.2 2.1.1 2002 PSF yes
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# 2.1.3 2.1.2 2002 PSF yes
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# 2.2.1 2.2 2002 PSF yes
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# 2.2.2 2.2.1 2002 PSF yes
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# 2.2.3 2.2.2 2003 PSF yes
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# 2.3 2.2.2 2002-2003 PSF yes
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# 2.3.1 2.3 2002-2003 PSF yes
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# 2.3.2 2.3.1 2002-2003 PSF yes
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# 2.3.3 2.3.2 2002-2003 PSF yes
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# 2.3.4 2.3.3 2004 PSF yes
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# 2.3.5 2.3.4 2005 PSF yes
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# 2.4 2.3 2004 PSF yes
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# 2.4.1 2.4 2005 PSF yes
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# 2.4.2 2.4.1 2005 PSF yes
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# 2.4.3 2.4.2 2006 PSF yes
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# 2.4.4 2.4.3 2006 PSF yes
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# 2.5 2.4 2006 PSF yes
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# 2.5.1 2.5 2007 PSF yes
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# 2.5.2 2.5.1 2008 PSF yes
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# 2.5.3 2.5.2 2008 PSF yes
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# 2.6 2.5 2008 PSF yes
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# 2.6.1 2.6 2008 PSF yes
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# 2.6.2 2.6.1 2009 PSF yes
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# 2.6.3 2.6.2 2009 PSF yes
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# 2.6.4 2.6.3 2009 PSF yes
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# 2.6.5 2.6.4 2010 PSF yes
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# 2.7 2.6 2010 PSF yes
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#
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# Footnotes:
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#
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# (1) GPL-compatible doesn't mean that we're distributing Python under
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# the GPL. All Python licenses, unlike the GPL, let you distribute
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# a modified version without making your changes open source. The
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# GPL-compatible licenses make it possible to combine Python with
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# other software that is released under the GPL; the others don't.
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#
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# (2) According to Richard Stallman, 1.6.1 is not GPL-compatible,
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# because its license has a choice of law clause. According to
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# CNRI, however, Stallman's lawyer has told CNRI's lawyer that 1.6.1
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# is "not incompatible" with the GPL.
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#
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# Thanks to the many outside volunteers who have worked under Guido's
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# direction to make these releases possible.
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#
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#
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# B. TERMS AND CONDITIONS FOR ACCESSING OR OTHERWISE USING PYTHON
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# ===============================================================
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#
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# PYTHON SOFTWARE FOUNDATION LICENSE VERSION 2
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# --------------------------------------------
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#
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# 1. This LICENSE AGREEMENT is between the Python Software Foundation
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# ("PSF"), and the Individual or Organization ("Licensee") accessing and
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# otherwise using this software ("Python") in source or binary form and
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# its associated documentation.
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#
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# 2. Subject to the terms and conditions of this License Agreement, PSF hereby
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# grants Licensee a nonexclusive, royalty-free, world-wide license to reproduce,
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# analyze, test, perform and/or display publicly, prepare derivative works,
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# distribute, and otherwise use Python alone or in any derivative version,
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# provided, however, that PSF's License Agreement and PSF's notice of copyright,
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# i.e., "Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
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# 2011, 2012, 2013 Python Software Foundation; All Rights Reserved" are retained
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# in Python alone or in any derivative version prepared by Licensee.
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#
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# 3. In the event Licensee prepares a derivative work that is based on
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# or incorporates Python or any part thereof, and wants to make
|
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# the derivative work available to others as provided herein, then
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# Licensee hereby agrees to include in any such work a brief summary of
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# the changes made to Python.
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#
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# 4. PSF is making Python available to Licensee on an "AS IS"
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# basis. PSF MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
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# IMPLIED. BY WAY OF EXAMPLE, BUT NOT LIMITATION, PSF MAKES NO AND
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# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
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# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON WILL NOT
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# INFRINGE ANY THIRD PARTY RIGHTS.
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#
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# 5. PSF SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
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# FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
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# A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON,
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# OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
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#
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# 6. This License Agreement will automatically terminate upon a material
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# breach of its terms and conditions.
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#
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# 7. Nothing in this License Agreement shall be deemed to create any
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# relationship of agency, partnership, or joint venture between PSF and
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# Licensee. This License Agreement does not grant permission to use PSF
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# trademarks or trade name in a trademark sense to endorse or promote
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# products or services of Licensee, or any third party.
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#
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# 8. By copying, installing or otherwise using Python, Licensee
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# agrees to be bound by the terms and conditions of this License
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# Agreement.
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#
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#
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# BEOPEN.COM LICENSE AGREEMENT FOR PYTHON 2.0
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# -------------------------------------------
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#
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# BEOPEN PYTHON OPEN SOURCE LICENSE AGREEMENT VERSION 1
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#
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# 1. This LICENSE AGREEMENT is between BeOpen.com ("BeOpen"), having an
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# office at 160 Saratoga Avenue, Santa Clara, CA 95051, and the
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# Individual or Organization ("Licensee") accessing and otherwise using
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# this software in source or binary form and its associated
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# documentation ("the Software").
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#
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# 2. Subject to the terms and conditions of this BeOpen Python License
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# Agreement, BeOpen hereby grants Licensee a non-exclusive,
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# royalty-free, world-wide license to reproduce, analyze, test, perform
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# and/or display publicly, prepare derivative works, distribute, and
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# otherwise use the Software alone or in any derivative version,
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# provided, however, that the BeOpen Python License is retained in the
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# Software, alone or in any derivative version prepared by Licensee.
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#
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# 3. BeOpen is making the Software available to Licensee on an "AS IS"
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# basis. BEOPEN MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
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# IMPLIED. BY WAY OF EXAMPLE, BUT NOT LIMITATION, BEOPEN MAKES NO AND
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# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
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# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF THE SOFTWARE WILL NOT
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# INFRINGE ANY THIRD PARTY RIGHTS.
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#
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# 4. BEOPEN SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF THE
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# SOFTWARE FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS
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# AS A RESULT OF USING, MODIFYING OR DISTRIBUTING THE SOFTWARE, OR ANY
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# DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
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#
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# 5. This License Agreement will automatically terminate upon a material
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# breach of its terms and conditions.
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#
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# 6. This License Agreement shall be governed by and interpreted in all
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# respects by the law of the State of California, excluding conflict of
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# law provisions. Nothing in this License Agreement shall be deemed to
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# create any relationship of agency, partnership, or joint venture
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# between BeOpen and Licensee. This License Agreement does not grant
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# permission to use BeOpen trademarks or trade names in a trademark
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# sense to endorse or promote products or services of Licensee, or any
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# third party. As an exception, the "BeOpen Python" logos available at
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# http://www.pythonlabs.com/logos.html may be used according to the
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# permissions granted on that web page.
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#
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# 7. By copying, installing or otherwise using the software, Licensee
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# agrees to be bound by the terms and conditions of this License
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# Agreement.
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#
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#
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# CNRI LICENSE AGREEMENT FOR PYTHON 1.6.1
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# ---------------------------------------
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#
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# 1. This LICENSE AGREEMENT is between the Corporation for National
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# Research Initiatives, having an office at 1895 Preston White Drive,
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# Reston, VA 20191 ("CNRI"), and the Individual or Organization
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# ("Licensee") accessing and otherwise using Python 1.6.1 software in
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# source or binary form and its associated documentation.
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#
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# 2. Subject to the terms and conditions of this License Agreement, CNRI
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# hereby grants Licensee a nonexclusive, royalty-free, world-wide
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# license to reproduce, analyze, test, perform and/or display publicly,
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# prepare derivative works, distribute, and otherwise use Python 1.6.1
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# alone or in any derivative version, provided, however, that CNRI's
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# License Agreement and CNRI's notice of copyright, i.e., "Copyright (c)
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# 1995-2001 Corporation for National Research Initiatives; All Rights
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# Reserved" are retained in Python 1.6.1 alone or in any derivative
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# version prepared by Licensee. Alternately, in lieu of CNRI's License
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# Agreement, Licensee may substitute the following text (omitting the
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# quotes): "Python 1.6.1 is made available subject to the terms and
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# conditions in CNRI's License Agreement. This Agreement together with
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# Python 1.6.1 may be located on the Internet using the following
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# unique, persistent identifier (known as a handle): 1895.22/1013. This
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# Agreement may also be obtained from a proxy server on the Internet
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# using the following URL: http://hdl.handle.net/1895.22/1013".
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#
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# 3. In the event Licensee prepares a derivative work that is based on
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# or incorporates Python 1.6.1 or any part thereof, and wants to make
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# the derivative work available to others as provided herein, then
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# Licensee hereby agrees to include in any such work a brief summary of
|
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# the changes made to Python 1.6.1.
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#
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# 4. CNRI is making Python 1.6.1 available to Licensee on an "AS IS"
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# basis. CNRI MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
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# IMPLIED. BY WAY OF EXAMPLE, BUT NOT LIMITATION, CNRI MAKES NO AND
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# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
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# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON 1.6.1 WILL NOT
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# INFRINGE ANY THIRD PARTY RIGHTS.
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#
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# 5. CNRI SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
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# 1.6.1 FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
|
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# A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON 1.6.1,
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# OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
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#
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# 6. This License Agreement will automatically terminate upon a material
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# breach of its terms and conditions.
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#
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# 7. This License Agreement shall be governed by the federal
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# intellectual property law of the United States, including without
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# limitation the federal copyright law, and, to the extent such
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# U.S. federal law does not apply, by the law of the Commonwealth of
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# Virginia, excluding Virginia's conflict of law provisions.
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# Notwithstanding the foregoing, with regard to derivative works based
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# on Python 1.6.1 that incorporate non-separable material that was
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# previously distributed under the GNU General Public License (GPL), the
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# law of the Commonwealth of Virginia shall govern this License
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# Agreement only as to issues arising under or with respect to
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# Paragraphs 4, 5, and 7 of this License Agreement. Nothing in this
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# License Agreement shall be deemed to create any relationship of
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# agency, partnership, or joint venture between CNRI and Licensee. This
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# License Agreement does not grant permission to use CNRI trademarks or
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# trade name in a trademark sense to endorse or promote products or
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# services of Licensee, or any third party.
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#
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# 8. By clicking on the "ACCEPT" button where indicated, or by copying,
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# installing or otherwise using Python 1.6.1, Licensee agrees to be
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# bound by the terms and conditions of this License Agreement.
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#
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# ACCEPT
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#
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#
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# CWI LICENSE AGREEMENT FOR PYTHON 0.9.0 THROUGH 1.2
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# --------------------------------------------------
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#
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# Copyright (c) 1991 - 1995, Stichting Mathematisch Centrum Amsterdam,
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# The Netherlands. All rights reserved.
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#
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# Permission to use, copy, modify, and distribute this software and its
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# documentation for any purpose and without fee is hereby granted,
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# provided that the above copyright notice appear in all copies and that
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# both that copyright notice and this permission notice appear in
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# supporting documentation, and that the name of Stichting Mathematisch
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# Centrum or CWI not be used in advertising or publicity pertaining to
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# distribution of the software without specific, written prior
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# permission.
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#
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# STICHTING MATHEMATISCH CENTRUM DISCLAIMS ALL WARRANTIES WITH REGARD TO
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# THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
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# FITNESS, IN NO EVENT SHALL STICHTING MATHEMATISCH CENTRUM BE LIABLE
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# FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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# WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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# ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT
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# OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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"""Heap queue algorithm (a.k.a. priority queue).
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Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
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all k, counting elements from 0. For the sake of comparison,
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non-existing elements are considered to be infinite. The interesting
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property of a heap is that a[0] is always its smallest element.
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Usage:
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heap = [] # creates an empty heap
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heappush(heap, item) # pushes a new item on the heap
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item = heappop(heap) # pops the smallest item from the heap
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item = heap[0] # smallest item on the heap without popping it
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heapify(x) # transforms list into a heap, in-place, in linear time
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item = heapreplace(heap, item) # pops and returns smallest item, and adds
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# new item; the heap size is unchanged
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Our API differs from textbook heap algorithms as follows:
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- We use 0-based indexing. This makes the relationship between the
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index for a node and the indexes for its children slightly less
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obvious, but is more suitable since Python uses 0-based indexing.
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- Our heappop() method returns the smallest item, not the largest.
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These two make it possible to view the heap as a regular Python list
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without surprises: heap[0] is the smallest item, and heap.sort()
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maintains the heap invariant!
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"""
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# Original code by Kevin O'Connor, augmented by Tim Peters and Raymond Hettinger
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__about__ = """Heap queues
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[explanation by François Pinard]
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Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
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all k, counting elements from 0. For the sake of comparison,
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non-existing elements are considered to be infinite. The interesting
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property of a heap is that a[0] is always its smallest element.
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The strange invariant above is meant to be an efficient memory
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representation for a tournament. The numbers below are `k', not a[k]:
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0
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1 2
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3 4 5 6
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7 8 9 10 11 12 13 14
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15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
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In the tree above, each cell `k' is topping `2*k+1' and `2*k+2'. In
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an usual binary tournament we see in sports, each cell is the winner
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over the two cells it tops, and we can trace the winner down the tree
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to see all opponents s/he had. However, in many computer applications
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of such tournaments, we do not need to trace the history of a winner.
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To be more memory efficient, when a winner is promoted, we try to
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replace it by something else at a lower level, and the rule becomes
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that a cell and the two cells it tops contain three different items,
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but the top cell "wins" over the two topped cells.
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If this heap invariant is protected at all time, index 0 is clearly
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the overall winner. The simplest algorithmic way to remove it and
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find the "next" winner is to move some loser (let's say cell 30 in the
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|
diagram above) into the 0 position, and then percolate this new 0 down
|
|
the tree, exchanging values, until the invariant is re-established.
|
|
This is clearly logarithmic on the total number of items in the tree.
|
|
By iterating over all items, you get an O(n ln n) sort.
|
|
|
|
A nice feature of this sort is that you can efficiently insert new
|
|
items while the sort is going on, provided that the inserted items are
|
|
not "better" than the last 0'th element you extracted. This is
|
|
especially useful in simulation contexts, where the tree holds all
|
|
incoming events, and the "win" condition means the smallest scheduled
|
|
time. When an event schedule other events for execution, they are
|
|
scheduled into the future, so they can easily go into the heap. So, a
|
|
heap is a good structure for implementing schedulers (this is what I
|
|
used for my MIDI sequencer :-).
|
|
|
|
Various structures for implementing schedulers have been extensively
|
|
studied, and heaps are good for this, as they are reasonably speedy,
|
|
the speed is almost constant, and the worst case is not much different
|
|
than the average case. However, there are other representations which
|
|
are more efficient overall, yet the worst cases might be terrible.
|
|
|
|
Heaps are also very useful in big disk sorts. You most probably all
|
|
know that a big sort implies producing "runs" (which are pre-sorted
|
|
sequences, which size is usually related to the amount of CPU memory),
|
|
followed by a merging passes for these runs, which merging is often
|
|
very cleverly organised[1]. It is very important that the initial
|
|
sort produces the longest runs possible. Tournaments are a good way
|
|
to that. If, using all the memory available to hold a tournament, you
|
|
replace and percolate items that happen to fit the current run, you'll
|
|
produce runs which are twice the size of the memory for random input,
|
|
and much better for input fuzzily ordered.
|
|
|
|
Moreover, if you output the 0'th item on disk and get an input which
|
|
may not fit in the current tournament (because the value "wins" over
|
|
the last output value), it cannot fit in the heap, so the size of the
|
|
heap decreases. The freed memory could be cleverly reused immediately
|
|
for progressively building a second heap, which grows at exactly the
|
|
same rate the first heap is melting. When the first heap completely
|
|
vanishes, you switch heaps and start a new run. Clever and quite
|
|
effective!
|
|
|
|
In a word, heaps are useful memory structures to know. I use them in
|
|
a few applications, and I think it is good to keep a `heap' module
|
|
around. :-)
|
|
|
|
--------------------
|
|
[1] The disk balancing algorithms which are current, nowadays, are
|
|
more annoying than clever, and this is a consequence of the seeking
|
|
capabilities of the disks. On devices which cannot seek, like big
|
|
tape drives, the story was quite different, and one had to be very
|
|
clever to ensure (far in advance) that each tape movement will be the
|
|
most effective possible (that is, will best participate at
|
|
"progressing" the merge). Some tapes were even able to read
|
|
backwards, and this was also used to avoid the rewinding time.
|
|
Believe me, real good tape sorts were quite spectacular to watch!
|
|
From all times, sorting has always been a Great Art! :-)
|
|
"""
|
|
|
|
__all__ = ['heappush', 'heappop', 'heapify', 'heapreplace', 'merge',
|
|
'nlargest', 'nsmallest', 'heappushpop']
|
|
|
|
def heappush(heap, item):
|
|
"""Push item onto heap, maintaining the heap invariant."""
|
|
heap.append(item)
|
|
_siftdown(heap, 0, len(heap)-1)
|
|
|
|
def heappop(heap):
|
|
"""Pop the smallest item off the heap, maintaining the heap invariant."""
|
|
lastelt = heap.pop() # raises appropriate IndexError if heap is empty
|
|
if heap:
|
|
returnitem = heap[0]
|
|
heap[0] = lastelt
|
|
_siftup(heap, 0)
|
|
return returnitem
|
|
return lastelt
|
|
|
|
def heapreplace(heap, item):
|
|
"""Pop and return the current smallest value, and add the new item.
|
|
|
|
This is more efficient than heappop() followed by heappush(), and can be
|
|
more appropriate when using a fixed-size heap. Note that the value
|
|
returned may be larger than item! That constrains reasonable uses of
|
|
this routine unless written as part of a conditional replacement:
|
|
|
|
if item > heap[0]:
|
|
item = heapreplace(heap, item)
|
|
"""
|
|
returnitem = heap[0] # raises appropriate IndexError if heap is empty
|
|
heap[0] = item
|
|
_siftup(heap, 0)
|
|
return returnitem
|
|
|
|
def heappushpop(heap, item):
|
|
"""Fast version of a heappush followed by a heappop."""
|
|
if heap and heap[0] < item:
|
|
item, heap[0] = heap[0], item
|
|
_siftup(heap, 0)
|
|
return item
|
|
|
|
def heapify(x):
|
|
"""Transform list into a heap, in-place, in O(len(x)) time."""
|
|
n = len(x)
|
|
# Transform bottom-up. The largest index there's any point to looking at
|
|
# is the largest with a child index in-range, so must have 2*i + 1 < n,
|
|
# or i < (n-1)/2. If n is even = 2*j, this is (2*j-1)/2 = j-1/2 so
|
|
# j-1 is the largest, which is n//2 - 1. If n is odd = 2*j+1, this is
|
|
# (2*j+1-1)/2 = j so j-1 is the largest, and that's again n//2-1.
|
|
for i in reversed(range(n//2)):
|
|
_siftup(x, i)
|
|
|
|
def _heappop_max(heap):
|
|
"""Maxheap version of a heappop."""
|
|
lastelt = heap.pop() # raises appropriate IndexError if heap is empty
|
|
if heap:
|
|
returnitem = heap[0]
|
|
heap[0] = lastelt
|
|
_siftup_max(heap, 0)
|
|
return returnitem
|
|
return lastelt
|
|
|
|
def _heapreplace_max(heap, item):
|
|
"""Maxheap version of a heappop followed by a heappush."""
|
|
returnitem = heap[0] # raises appropriate IndexError if heap is empty
|
|
heap[0] = item
|
|
_siftup_max(heap, 0)
|
|
return returnitem
|
|
|
|
def _heapify_max(x):
|
|
"""Transform list into a maxheap, in-place, in O(len(x)) time."""
|
|
n = len(x)
|
|
for i in reversed(range(n//2)):
|
|
_siftup_max(x, i)
|
|
|
|
# 'heap' is a heap at all indices >= startpos, except possibly for pos. pos
|
|
# is the index of a leaf with a possibly out-of-order value. Restore the
|
|
# heap invariant.
|
|
def _siftdown(heap, startpos, pos):
|
|
newitem = heap[pos]
|
|
# Follow the path to the root, moving parents down until finding a place
|
|
# newitem fits.
|
|
while pos > startpos:
|
|
parentpos = (pos - 1) >> 1
|
|
parent = heap[parentpos]
|
|
if newitem < parent:
|
|
heap[pos] = parent
|
|
pos = parentpos
|
|
continue
|
|
break
|
|
heap[pos] = newitem
|
|
|
|
# The child indices of heap index pos are already heaps, and we want to make
|
|
# a heap at index pos too. We do this by bubbling the smaller child of
|
|
# pos up (and so on with that child's children, etc) until hitting a leaf,
|
|
# then using _siftdown to move the oddball originally at index pos into place.
|
|
#
|
|
# We *could* break out of the loop as soon as we find a pos where newitem <=
|
|
# both its children, but turns out that's not a good idea, and despite that
|
|
# many books write the algorithm that way. During a heap pop, the last array
|
|
# element is sifted in, and that tends to be large, so that comparing it
|
|
# against values starting from the root usually doesn't pay (= usually doesn't
|
|
# get us out of the loop early). See Knuth, Volume 3, where this is
|
|
# explained and quantified in an exercise.
|
|
#
|
|
# Cutting the # of comparisons is important, since these routines have no
|
|
# way to extract "the priority" from an array element, so that intelligence
|
|
# is likely to be hiding in custom comparison methods, or in array elements
|
|
# storing (priority, record) tuples. Comparisons are thus potentially
|
|
# expensive.
|
|
#
|
|
# On random arrays of length 1000, making this change cut the number of
|
|
# comparisons made by heapify() a little, and those made by exhaustive
|
|
# heappop() a lot, in accord with theory. Here are typical results from 3
|
|
# runs (3 just to demonstrate how small the variance is):
|
|
#
|
|
# Compares needed by heapify Compares needed by 1000 heappops
|
|
# -------------------------- --------------------------------
|
|
# 1837 cut to 1663 14996 cut to 8680
|
|
# 1855 cut to 1659 14966 cut to 8678
|
|
# 1847 cut to 1660 15024 cut to 8703
|
|
#
|
|
# Building the heap by using heappush() 1000 times instead required
|
|
# 2198, 2148, and 2219 compares: heapify() is more efficient, when
|
|
# you can use it.
|
|
#
|
|
# The total compares needed by list.sort() on the same lists were 8627,
|
|
# 8627, and 8632 (this should be compared to the sum of heapify() and
|
|
# heappop() compares): list.sort() is (unsurprisingly!) more efficient
|
|
# for sorting.
|
|
|
|
def _siftup(heap, pos):
|
|
endpos = len(heap)
|
|
startpos = pos
|
|
newitem = heap[pos]
|
|
# Bubble up the smaller child until hitting a leaf.
|
|
childpos = 2*pos + 1 # leftmost child position
|
|
while childpos < endpos:
|
|
# Set childpos to index of smaller child.
|
|
rightpos = childpos + 1
|
|
if rightpos < endpos and not heap[childpos] < heap[rightpos]:
|
|
childpos = rightpos
|
|
# Move the smaller child up.
|
|
heap[pos] = heap[childpos]
|
|
pos = childpos
|
|
childpos = 2*pos + 1
|
|
# The leaf at pos is empty now. Put newitem there, and bubble it up
|
|
# to its final resting place (by sifting its parents down).
|
|
heap[pos] = newitem
|
|
_siftdown(heap, startpos, pos)
|
|
|
|
def _siftdown_max(heap, startpos, pos):
|
|
'Maxheap variant of _siftdown'
|
|
newitem = heap[pos]
|
|
# Follow the path to the root, moving parents down until finding a place
|
|
# newitem fits.
|
|
while pos > startpos:
|
|
parentpos = (pos - 1) >> 1
|
|
parent = heap[parentpos]
|
|
if parent < newitem:
|
|
heap[pos] = parent
|
|
pos = parentpos
|
|
continue
|
|
break
|
|
heap[pos] = newitem
|
|
|
|
def _siftup_max(heap, pos):
|
|
'Maxheap variant of _siftup'
|
|
endpos = len(heap)
|
|
startpos = pos
|
|
newitem = heap[pos]
|
|
# Bubble up the larger child until hitting a leaf.
|
|
childpos = 2*pos + 1 # leftmost child position
|
|
while childpos < endpos:
|
|
# Set childpos to index of larger child.
|
|
rightpos = childpos + 1
|
|
if rightpos < endpos and not heap[rightpos] < heap[childpos]:
|
|
childpos = rightpos
|
|
# Move the larger child up.
|
|
heap[pos] = heap[childpos]
|
|
pos = childpos
|
|
childpos = 2*pos + 1
|
|
# The leaf at pos is empty now. Put newitem there, and bubble it up
|
|
# to its final resting place (by sifting its parents down).
|
|
heap[pos] = newitem
|
|
_siftdown_max(heap, startpos, pos)
|
|
|
|
def merge(iterables, key=None, reverse=False):
|
|
'''Merge multiple sorted inputs into a single sorted output.
|
|
|
|
Similar to sorted(itertools.chain(*iterables)) but returns a generator,
|
|
does not pull the data into memory all at once, and assumes that each of
|
|
the input streams is already sorted (smallest to largest).
|
|
|
|
>>> list(merge([1,3,5,7], [0,2,4,8], [5,10,15,20], [], [25]))
|
|
[0, 1, 2, 3, 4, 5, 5, 7, 8, 10, 15, 20, 25]
|
|
|
|
If *key* is not None, applies a key function to each element to determine
|
|
its sort order.
|
|
|
|
>>> list(merge(['dog', 'horse'], ['cat', 'fish', 'kangaroo'], key=len))
|
|
['dog', 'cat', 'fish', 'horse', 'kangaroo']
|
|
|
|
'''
|
|
|
|
h = []
|
|
h_append = h.append
|
|
|
|
if reverse:
|
|
_heapify = _heapify_max
|
|
_heappop = _heappop_max
|
|
_heapreplace = _heapreplace_max
|
|
direction = -1
|
|
else:
|
|
_heapify = heapify
|
|
_heappop = heappop
|
|
_heapreplace = heapreplace
|
|
direction = 1
|
|
|
|
if key is None:
|
|
for order, it in enumerate(map(iter, iterables)):
|
|
try:
|
|
h_append([next(it), order * direction, it])
|
|
except StopIteration:
|
|
pass
|
|
_heapify(h)
|
|
while len(h) > 1:
|
|
try:
|
|
while True:
|
|
value, order, it = s = h[0]
|
|
yield value
|
|
s[0] = next(it) # raises StopIteration when exhausted
|
|
_heapreplace(h, s) # restore heap condition
|
|
except StopIteration:
|
|
_heappop(h) # remove empty iterator
|
|
if h:
|
|
# fast case when only a single iterator remains
|
|
value, order, it = h[0]
|
|
yield value
|
|
for value in it:
|
|
yield value
|
|
return
|
|
|
|
for order, it in enumerate(map(iter, iterables)):
|
|
try:
|
|
value = next(it)
|
|
h_append([key(value), order * direction, value, it])
|
|
except StopIteration:
|
|
pass
|
|
_heapify(h)
|
|
while len(h) > 1:
|
|
try:
|
|
while True:
|
|
key_value, order, value, it = s = h[0]
|
|
yield value
|
|
value = next(it)
|
|
s[0] = key(value)
|
|
s[2] = value
|
|
_heapreplace(h, s)
|
|
except StopIteration:
|
|
_heappop(h)
|
|
if h:
|
|
key_value, order, value, it = h[0]
|
|
yield value
|
|
for value in it:
|
|
yield value
|
|
|
|
|
|
# Algorithm notes for nlargest() and nsmallest()
|
|
# ==============================================
|
|
#
|
|
# Make a single pass over the data while keeping the k most extreme values
|
|
# in a heap. Memory consumption is limited to keeping k values in a list.
|
|
#
|
|
# Measured performance for random inputs:
|
|
#
|
|
# number of comparisons
|
|
# n inputs k-extreme values (average of 5 trials) % more than min()
|
|
# ------------- ---------------- --------------------- -----------------
|
|
# 1,000 100 3,317 231.7%
|
|
# 10,000 100 14,046 40.5%
|
|
# 100,000 100 105,749 5.7%
|
|
# 1,000,000 100 1,007,751 0.8%
|
|
# 10,000,000 100 10,009,401 0.1%
|
|
#
|
|
# Theoretical number of comparisons for k smallest of n random inputs:
|
|
#
|
|
# Step Comparisons Action
|
|
# ---- -------------------------- ---------------------------
|
|
# 1 1.66 * k heapify the first k-inputs
|
|
# 2 n - k compare remaining elements to top of heap
|
|
# 3 k * (1 + lg2(k)) * ln(n/k) replace the topmost value on the heap
|
|
# 4 k * lg2(k) - (k/2) final sort of the k most extreme values
|
|
#
|
|
# Combining and simplifying for a rough estimate gives:
|
|
#
|
|
# comparisons = n + k * (log(k, 2) * log(n/k) + log(k, 2) + log(n/k))
|
|
#
|
|
# Computing the number of comparisons for step 3:
|
|
# -----------------------------------------------
|
|
# * For the i-th new value from the iterable, the probability of being in the
|
|
# k most extreme values is k/i. For example, the probability of the 101st
|
|
# value seen being in the 100 most extreme values is 100/101.
|
|
# * If the value is a new extreme value, the cost of inserting it into the
|
|
# heap is 1 + log(k, 2).
|
|
# * The probabilty times the cost gives:
|
|
# (k/i) * (1 + log(k, 2))
|
|
# * Summing across the remaining n-k elements gives:
|
|
# sum((k/i) * (1 + log(k, 2)) for i in range(k+1, n+1))
|
|
# * This reduces to:
|
|
# (H(n) - H(k)) * k * (1 + log(k, 2))
|
|
# * Where H(n) is the n-th harmonic number estimated by:
|
|
# gamma = 0.5772156649
|
|
# H(n) = log(n, e) + gamma + 1 / (2 * n)
|
|
# http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)#Rate_of_divergence
|
|
# * Substituting the H(n) formula:
|
|
# comparisons = k * (1 + log(k, 2)) * (log(n/k, e) + (1/n - 1/k) / 2)
|
|
#
|
|
# Worst-case for step 3:
|
|
# ----------------------
|
|
# In the worst case, the input data is reversed sorted so that every new element
|
|
# must be inserted in the heap:
|
|
#
|
|
# comparisons = 1.66 * k + log(k, 2) * (n - k)
|
|
#
|
|
# Alternative Algorithms
|
|
# ----------------------
|
|
# Other algorithms were not used because they:
|
|
# 1) Took much more auxiliary memory,
|
|
# 2) Made multiple passes over the data.
|
|
# 3) Made more comparisons in common cases (small k, large n, semi-random input).
|
|
# See the more detailed comparison of approach at:
|
|
# http://code.activestate.com/recipes/577573-compare-algorithms-for-heapqsmallest
|
|
|
|
def nsmallest(n, iterable, key=None):
|
|
"""Find the n smallest elements in a dataset.
|
|
|
|
Equivalent to: sorted(iterable, key=key)[:n]
|
|
"""
|
|
|
|
# Short-cut for n==1 is to use min()
|
|
if n == 1:
|
|
it = iter(iterable)
|
|
sentinel = object()
|
|
if key is None:
|
|
result = min(it, default=sentinel)
|
|
else:
|
|
result = min(it, default=sentinel, key=key)
|
|
return [] if result is sentinel else [result]
|
|
|
|
# When n>=size, it's faster to use sorted()
|
|
try:
|
|
size = len(iterable)
|
|
except (TypeError, AttributeError):
|
|
pass
|
|
else:
|
|
if n >= size:
|
|
return sorted(iterable, key=key)[:n]
|
|
|
|
# When key is none, use simpler decoration
|
|
if key is None:
|
|
it = iter(iterable)
|
|
# put the range(n) first so that zip() doesn't
|
|
# consume one too many elements from the iterator
|
|
result = [(elem, i) for i, elem in zip(range(n), it)]
|
|
if not result:
|
|
return result
|
|
_heapify_max(result)
|
|
top = result[0][0]
|
|
order = n
|
|
_heapreplace = _heapreplace_max
|
|
for elem in it:
|
|
if elem < top:
|
|
_heapreplace(result, (elem, order))
|
|
top = result[0][0]
|
|
order += 1
|
|
result.sort()
|
|
return [r[0] for r in result]
|
|
|
|
# General case, slowest method
|
|
it = iter(iterable)
|
|
result = [(key(elem), i, elem) for i, elem in zip(range(n), it)]
|
|
if not result:
|
|
return result
|
|
_heapify_max(result)
|
|
top = result[0][0]
|
|
order = n
|
|
_heapreplace = _heapreplace_max
|
|
for elem in it:
|
|
k = key(elem)
|
|
if k < top:
|
|
_heapreplace(result, (k, order, elem))
|
|
top = result[0][0]
|
|
order += 1
|
|
result.sort()
|
|
return [r[2] for r in result]
|
|
|
|
def nlargest(n, iterable, key=None):
|
|
"""Find the n largest elements in a dataset.
|
|
|
|
Equivalent to: sorted(iterable, key=key, reverse=True)[:n]
|
|
"""
|
|
|
|
# Short-cut for n==1 is to use max()
|
|
if n == 1:
|
|
it = iter(iterable)
|
|
sentinel = object()
|
|
if key is None:
|
|
result = max(it, default=sentinel)
|
|
else:
|
|
result = max(it, default=sentinel, key=key)
|
|
return [] if result is sentinel else [result]
|
|
|
|
# When n>=size, it's faster to use sorted()
|
|
try:
|
|
size = len(iterable)
|
|
except (TypeError, AttributeError):
|
|
pass
|
|
else:
|
|
if n >= size:
|
|
return sorted(iterable, key=key, reverse=True)[:n]
|
|
|
|
# When key is none, use simpler decoration
|
|
if key is None:
|
|
it = iter(iterable)
|
|
result = [(elem, i) for i, elem in zip(range(0, -n, -1), it)]
|
|
if not result:
|
|
return result
|
|
heapify(result)
|
|
top = result[0][0]
|
|
order = -n
|
|
_heapreplace = heapreplace
|
|
for elem in it:
|
|
if top < elem:
|
|
_heapreplace(result, (elem, order))
|
|
top = result[0][0]
|
|
order -= 1
|
|
result.sort(reverse=True)
|
|
return [r[0] for r in result]
|
|
|
|
# General case, slowest method
|
|
it = iter(iterable)
|
|
result = [(key(elem), i, elem) for i, elem in zip(range(0, -n, -1), it)]
|
|
if not result:
|
|
return result
|
|
heapify(result)
|
|
top = result[0][0]
|
|
order = -n
|
|
_heapreplace = heapreplace
|
|
for elem in it:
|
|
k = key(elem)
|
|
if top < k:
|
|
_heapreplace(result, (k, order, elem))
|
|
top = result[0][0]
|
|
order -= 1
|
|
result.sort(reverse=True)
|
|
return [r[2] for r in result]
|
|
|
|
# If available, use C implementation
|
|
try:
|
|
from _heapq import *
|
|
except ImportError:
|
|
pass
|
|
try:
|
|
from _heapq import _heapreplace_max
|
|
except ImportError:
|
|
pass
|
|
try:
|
|
from _heapq import _heapify_max
|
|
except ImportError:
|
|
pass
|
|
try:
|
|
from _heapq import _heappop_max
|
|
except ImportError:
|
|
pass
|
|
|
|
|
|
if __name__ == "__main__":
|
|
|
|
import doctest
|
|
print(doctest.testmod())
|